BPS Fivebrane Stars II: Fluctuations

We investigate quantum fluctuations of metric components in coherent 1/2-BPS bound states of $n_1$ fundamental strings and $n_5$ NS5-branes. The leading order contribution in an expansion in $1/(n_1n_5)$ is calculated via a combination of analytical and numerical methods. We find that the fluctuations are small away from a tiny distance from the source, comparable to the 6d Planck scale. Comparing this result with an analysis in the literature of fluctuations in the maximally mixed state, we conclude that the large fluctuations previously found for the latter are statistical rather than quantum in nature, and that perturbative string theory provides an accurate description of these backgrounds.